First off, thank you Peter for the recommendations of my articles.
It looks like there are a number of issues with your site. I wouldn't focus so much on just one algorithm, but rather, spend time looking at the entire site and its issues.
What phrases are you trying to rank for? Your title tag on your home page says, "The Community of Web Design Professionals" which I am guessing is not your money keyword. Keywords in the title tag (without stuffing), especially at the front of the tag are very important.
Next, I would get rid of the huge full page popup. It could possibly cause the page layout algo to affect your rankings. It can also cause people to quickly bounce away and look for another site which can be a signal to Google that users don't enjoy your site.
The Google pagespeed insights tool gives you a very low score. Improving on pagespeed could make a significant difference.
You've got 1490 pages in Google's index. Do you really have 1490 high quality pages? Is it possible that there is some content indexed that doesn't need to be? For example, when I take text from this article: http://www.1stwebdesigner.com/find-qualified-designer/ and search for it on quotes on Google I see 27 results. The only pages that you want from your site in Google's index are high quality, unique and compelling articles and resources. With that said, if you wrote this article and other people copied it, I wouldn't be worried. But, if you purposely syndicated it, then it could be an issue.
It's hard to say whether links are the issue. It doesn't seem like any of your drops coincided with a Penguin date so I am guessing that Penguin is not suppressing you. (Can't say for sure without having a deep look). But, it is possible that you were previously getting some benefit from self made links that now, Google can determine are self made as opposed to truly earned and they may be discounting those links. You mentioned that you had created a lot of links on your own. As Google gets better and better at figuring out which links are truly earned as opposed to self made, it may be that you've lost significant pagerank that used to come through these links.
With that said, have you checked Google Search Console --> Search Traffic --> Manual actions to make sure there is no manual action there? I see a lot of blogroll links and sometimes if there has been excessive link exchanging going on a site can get a manual action.
Now, back to the algo stuff. Can you tell via Google analytics if the big drop in May happened on May 20, 2014? If not, it's not Panda. If it is exactly on this date though, then I'd be spending more time looking at on-site issues than links.
Hope that helps!
Marie